Pure Survival Mode:
Enemies only drop resources, and there’s no ammo, health, or weapon parts to be found. Completion unlocks the MK-II Overclocked Parts Set and a Mega Resource Deposit.
New Game+:
New Game+ is unlocked after you complete the game once. Your inventory will stay the same, but your chapter progress is reset.
Hardcore Mode:
Hardcore mode is harder then the Hard and Impossible modes, you can only save three times during the entire campaign and you're limited to 1 existence.
Upon completion you unlock the "Devil Horns", a very special weapon, similar to the foam finger from Dead Space 2.
Retro Mode:
Complete Hardcore mode to unlock the Retro Mode.
Classic Mode:
The Classic Mode is a rewind to the original Dead Space. Single-player only, with no cross-hairs or any resource management elements.

Unlock Planet Cracker Plasma Cutter
Have a Dead Space 2 save-game available and you'll unlock the old Plasma Cutter.

Easy Trophy: "Under a Buck"
The Trophy "Under A Buck" is unlocked by shooting a stuffed deer head. In chapter 4 you are tasked with hacking a power console to an elevator.
Follow the waypoints and when you exit the elevator turn left to face the deer head. Shoot it.

Easy Trophy: "There's always Peng!"
During chapter 14, accept the optional mission "Reaper Barracks" when offered. During the mission you'll enter a pump room after taking a ladder down and skipping a spiked piston.
Just as you exit the pump tube, turn around to locate a machine called Pump 2. Use stasis to disable the pump after it's moved forward so you can see behind the piston, left of where you're standing.
When you see it, grab the Peng treasure from the left wall with Kinesis.